67 lines
2.3 KiB
C#
67 lines
2.3 KiB
C#
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using System.Collections;
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using System.Collections.Generic;
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using Unity.Mathematics;
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using static Unity.Mathematics.math;
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public class AetheriaMath
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{
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//first-order intercept using absolute target position
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public static float3 FirstOrderIntercept
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(
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float3 shooterPosition,
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float3 shooterVelocity,
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float shotSpeed,
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float3 targetPosition,
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float3 targetVelocity
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) {
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float3 targetRelativePosition = targetPosition - shooterPosition;
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float3 targetRelativeVelocity = targetVelocity - shooterVelocity;
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float t = FirstOrderInterceptTime
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(
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shotSpeed,
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targetRelativePosition,
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targetRelativeVelocity
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);
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return targetPosition + t*targetRelativeVelocity;
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}
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//first-order intercept using relative target position
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public static float FirstOrderInterceptTime
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(
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float shotSpeed,
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float3 targetRelativePosition,
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float3 targetRelativeVelocity
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) {
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float velocitySquared = lengthsq(targetRelativeVelocity);
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if(velocitySquared < 0.001f)
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return 0f;
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float a = velocitySquared - shotSpeed*shotSpeed;
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//handle similar velocities
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if (abs(a) < 0.001f)
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{
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float t = -lengthsq(targetRelativePosition)/ (2f*dot(targetRelativeVelocity, targetRelativePosition));
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return max(t, 0f); //don't shoot back in time
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}
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float b = 2f*dot(targetRelativeVelocity, targetRelativePosition);
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float c = lengthsq(targetRelativePosition);
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float determinant = b*b - 4f*a*c;
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if (determinant > 0f) { //determinant > 0; two intercept paths (most common)
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float t1 = (-b + sqrt(determinant))/(2f*a),
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t2 = (-b - sqrt(determinant))/(2f*a);
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if (t1 > 0f) {
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if (t2 > 0f)
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return min(t1, t2); //both are positive
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else
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return t1; //only t1 is positive
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} else
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return max(t2, 0f); //don't shoot back in time
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} else if (determinant < 0f) //determinant < 0; no intercept path
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return 0f;
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else //determinant = 0; one intercept path, pretty much never happens
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return max(-b/(2f*a), 0f); //don't shoot back in time
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}
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}
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